Knowledge of the concentration of hydroxyl radical is crucial to understanding the chemistry of the stratosphere. Hydroxyl participates in several catalytic cycles which destroy ozone and strongly influences the cycles of chlorine and nitrogen oxides by its reactions which form or destroy reservoirs for chlorine and odd-nitrogen compounds. We have measured the concentration of hydroxyl radical between the altitudes of 32.5 and 38.5 km using the technique of laser-induced fluorescence. Our results ranging from 4 to 9¿106 cm-3 (with an accuracy of ¿50%) are about 2--3 times lower than predicted by current one-dimensional models, although the uncertainties in our determination and in the models are sufficiently large to explain the differences. A number of potential improvements to the instrument are discussed.